> I expect that the way PLN accepts inconsistency would ultimately create deep > differences in the analysis, if we were being more rigorous about this. :) > Ignoring that issue...
Well, one way to look at it is -- the PLN inconsistency-handling has to do with the PLN rules' reflection of empirical data... -- OTOH the Gibbs sampling has to do with finding a set of truth values that are coherent with regard to the PLN rules as well as the given data So if the PLN inconsistency-handling is bad, this will affect the basic data that the Gibbs sampling has to work with, but won't affect its "correct" operation at finding something coherent w/ regard to the PLN rules... > I'm unsure why you're making this jump to 2nd-order samples. How does the > analogy to Gibbs sampling in MLNs work, in this version? Whether one uses first order distributional TVs or second order distributional TV doesn't matter..... Anyway I reverted the post to first order distributional TVs since the second order ones seemed to cause additional confusion... Actually I think second order is probably a better way to do it (recall that indefinite probabilities are summarized versions of second order distributions anyway), but that's irrelevant to the points of the blog post... > Also (getting even less formal), here's an intuitive problem I think might > come up with procedures of this general form. Since PLN inference is > estimating both weights and posterior probabilities in traditional graph > terms, it's as if we're doing Gibbs sampling over the weights as well as the > variable settings. This can work, but we need the entire dataset to stick > around in order for it to do the right thing: when we re-sample the > probability P(frisky|cat), we need the sample to be constrained by our > remembered instances of cats, in which case the resampling will almost > always yield something very close to the empirical ratio (because evidence > has concentrated probability mass in this area). For PLN, though, it may not > be feasible to keep around all the examples of everything in order to ensure > that the re-sampling is reasonable. We would prefer to keep just a summary > of the evidence we've seen, and get this to constrain the evidence in the > right way. Yeah --- note the two final sections I have added to the latest version of the post Gibbs sampling is based on the idea of convergence to the stationary distribution eventually, but in an AGI context one can never wait for "eventually", since there is always new data coming in, and old data being forgotten... However, it seems that if one does PLN in the standard way, as the personality parameter k goes to infinity one approximates Gibbs sampling.... So the possible practical suggestion I get from this theoretical excursion is: It might be interesting to maintain multiple truth values for an Atom, updated via different personality parameters... Kind of a "shaggy dog story" to get to that point via so much mathematical meandering, but that's how the creative process works sometimes ;) Also, I think there is a proof that trails are unnecessary in there somewhere (see the penultimate section). This is nice and is a difference btw PLN and NARS, though it's a weak conclusion in that it only really holds "in the long run" (so that trails may still be a good mechanism for averting some kinds of confused inference in the short run) Thanks so much for your feedback -- even if you don't fully grok my idea due to the compact/informal exposition, it's great to have *someone* read and comment with a significant level of understanding ;) -- Ben ------------------------------------------- AGI Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/21088071-f452e424 Modify Your Subscription: https://www.listbox.com/member/?member_id=21088071&id_secret=21088071-58d57657 Powered by Listbox: http://www.listbox.com
